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<h3 class="heading"><span class="type">Paragraph</span></h3>
<p>Suppose that <span class="process-math">\({\bf x}_1\)</span> is a particular solution to (<a href="" class="xref" data-knowl="./knowl/eq8_4.html" title="Equation 6.6.1">(6.6.1)</a>) and the general solution for</p>
<div class="displaymath process-math" data-contains-math-knowls="./knowl/eq8_4.html ./knowl/eq8_4.html">
\begin{equation}
{\bf x}^{\prime}={\bf P}(t)\,{\bf x},\quad \alpha \leq t \leq \beta,\tag{6.6.2}
\end{equation}
</div>
<p class="continuation">is</p>
<div class="displaymath process-math" data-contains-math-knowls="./knowl/eq8_4.html ./knowl/eq8_4.html">
\begin{equation*}
C_1 {\bf x}^{(1)}+C_2 {\bf x}^{(2)}+\cdots+C_n {\bf x}^{(n)}.
\end{equation*}
</div>
<p class="continuation">Then</p>
<div class="displaymath process-math" data-contains-math-knowls="./knowl/eq8_4.html ./knowl/eq8_4.html">
\begin{equation*}
{\bf x}=C_1 {\bf x}^{(1)}+C_2 {\bf x}^{(2)}+\cdots+C_n {\bf x}^{(n)}+{\bf x}_1
\end{equation*}
</div>
<p class="continuation">is the general solution to (<a href="" class="xref" data-knowl="./knowl/eq8_4.html" title="Equation 6.6.1">(6.6.1)</a>).</p>
<span class="incontext"><a href="sec6_6.html#p-284" class="internal">in-context</a></span>
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